The average California household's share of the debt for underfunded state and local government employee pensions comes to about $30,500.

Stanford University studies released last week and in December for the first time aggregate public pension shortfalls statewide. Using moderate assumptions about future investment returns, the unfunded liability is about $379 billion.

Hard-core pension reformers will maintain that the number is much more. Defenders of the status quo will insist it's significantly less. Before sorting out that dispute, let's understand what the numbers mean.

Each year public employees work, they increase their future pensions. So, as they work, they and their employers jointly should set aside enough money to cover the additional benefits.

To calculate the contributions, actuaries and pension boards make assumptions about future investment returns and pension costs. Unfortunately, they've been wrong.

They have overestimated investment earnings, underestimated pension costs and retroactively added benefits without proper funding. As a result, pension systems across California have huge unfunded liabilities.

Keep in mind that the shortfall is for pension benefits employees already earned. Like salary and health care benefits, it's a cost that should be paid when labor is performed.

Instead, the shortfall has been converted into debt to be paid off over time, up to 30 years. Government agencies make those payments, diverting money that would otherwise go for government services. So we're depriving current and future generations to pay off past labor costs.

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How much is the debt? It depends on how much pension systems project they can earn on investments. The greater the assumed rate of return, the less money pension systems need now and, hence, the smaller the shortfall. The converse is also true.

Most California public pension systems anticipate they can earn about 7.75 percent annually. Every year they fall short of that target they go deeper into debt.

The Stanford studies -- written by public policy professor Joe Nation, a former Democratic assemblyman, and math and economics student Evan Storms -- help us understand the absurdity of a 7.75 percent projection and the effects of different assumptions.

Using historical data from the nation's largest government pension fund, the California Public Employees' Retirement System, the Stanford team calculated the odds of meeting different investment return goals in the future and the effect of each rate on the statewide unfunded liability:

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When pension systems assume a 7.75 percent return rate, they have only a 42 percent chance of meeting or exceeding that target. But even using that optimistic assumption, the systems are currently only 77 percent funded, with a $180 billion shortfall. That averages $14,500 for each of California's 12.4 million households.

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Many argue that pension systems should base investment projections on much-less-risky bond rates, about 4.5 percent. The chance of reaching that goal is 81 percent. Using that rate, California pension systems are currently 48 percent funded, with a $658 billion shortfall, or about $53,000 per household.

Investment gurus such as Warren Buffett have argued for a midpoint, about 6.2 percent. The chance of reaching that goal is 63 percent. Using that rate, California systems are currently 61 percent funded, with a $379 billion shortfall, or about $30,500 per household.

Households won't receive individual bills for their shares. Instead, they will lose government services and face demands for more taxes. Using the midpoint assumption, the $379 billion debt is equal to about 3½ years of base salaries for state and local government employees. That's a lot of lost service.

The Stanford studies actually understate the magnitude of the problem. That's because many government agencies issued bonds and used that money to pay down their pension debts. But they are then left with bond debt. Those amounts are not included in the Stanford numbers.

Moreover, the numbers don't include the unfunded liability for promised retiree health benefits, which were estimated four years ago to be at least $118 billion. They're surely far more today.

Nevertheless, Nation and his students deserve huge credit for providing a comprehensive look at California's pension debt. State officials should have done it years ago.